Global Bifurcation Of Periodic Solutions With Symmetry

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Global Bifurcation Of Periodic Solutions With Symmetry

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Author : Bernold Fiedler
language : en
Publisher:
Release Date : 2014-01-15

Global Bifurcation Of Periodic Solutions With Symmetry written by Bernold Fiedler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Global Bifurcation Of Periodic Solutions With Symmetry

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Author : Bernold Fiedler
language : en
Publisher: Springer
Release Date : 2006-11-14

Global Bifurcation Of Periodic Solutions With Symmetry written by Bernold Fiedler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.

Dynamics Bifurcation And Symmetry

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Author : Pascal Chossat
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Dynamics Bifurcation And Symmetry written by Pascal Chossat and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.

Pattern Formation In Continuous And Coupled Systems

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Author : Martin Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Pattern Formation In Continuous And Coupled Systems written by Martin Golubitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz, Cornell University (Theoretical and Applied Mechan ics) for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Foundation (NSF), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE Pattern formation has been studied intensively for most of this cen tury by both experimentalists and theoreticians, and there have been many workshops and conferences devoted to the subject. In the IMA workshop on Pattern Formation in Continuous and Coupled Systems held May 11-15, 1998 we attempted to focus on new directions in the patterns literature.

Singularities And Groups In Bifurcation Theory

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Author : Martin Golubitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Singularities And Groups In Bifurcation Theory written by Martin Golubitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.

Degree Theory And Symmetric Equations Assisted By Gap System

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Author : Zalman Balanov
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-30

Degree Theory And Symmetric Equations Assisted By Gap System written by Zalman Balanov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Mathematics categories.

Symmetries are a common feature of real-world phenomena in many fields, including physics, biology, materials science, and engineering. They can help understand the behavior of a system and optimize engineering designs. Nonlinear effects such as delays, nonsmoothness, and hysteresis can have a significant impact on the dynamics and contribute to the increased complexity of symmetric systems. The goal of this book is to provide a complete theoretical and practical manual for studying a large class of dynamical problems with symmetries using degree theory methods. To study the impact of symmetries on the occurrence of periodic solutions in dynamical systems, special variants of the Brouwer degree, the Brouwer equivariant degree, and the twisted equivariant degree are developed to predict patterns, regularities, and symmetries of solutions. Applications to specific dynamical systems and examples are supported by a software package integrated with the GAP system, which provides assistance in the group-theoretic computations involved in equivariant analysis. This book is intended for readers with a basic knowledge of analysis and algebra, including researchers in pure and applied mathematical analysis, graduate students, and scientists interested in areas involving mathematical modeling of symmetric phenomena. The text is self-contained, and the necessary background material is provided in the appendices.

Dynamics And Symmetry

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Author : Michael J. Field
language : en
Publisher: Imperial College Press
Release Date : 2007

Dynamics And Symmetry written by Michael J. Field and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems. This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G -manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone. Sample Chapter(s). Chapter 1: Groups (309 KB). Contents: Groups; Group Actions and Representations; Smooth G -manifolds; Equivariant Bifurcation Theory: Steady State Bifurcation; Equivariant Bifurcation Theory: Dynamics; Equivariant Transversality; Applications of G -transversality to Bifurcation Theory I; Equivariant Dynamics; Dynamical Systems on G -manifolds; Applications of G -transversality to Bifurcation Theory II. Readership: Academics and graduate students in pure and applied mathematics.

Nonlinear Analysis And Optimization Ii

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Author : Simeon Reich
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Nonlinear Analysis And Optimization Ii written by Simeon Reich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This volume is the second of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in important fields of mathematics. This volume contains articles on optimization. Topics covered include the calculus of variations, constrained optimization problems, mathematical economics, metric regularity, nonsmooth analysis, optimal control, subdifferential calculus, time scales and transportation traffic. The companion volume (Contemporary Mathematics, Volume 513) is devoted to nonlinear analysis. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). Table of Contents: J.-P. Aubin and S. Martin -- Travel time tubes regulating transportation traffic; R. Baier and E. Farkhi -- The directed subdifferential of DC functions; Z. Balanov, W. Krawcewicz, and H. Ruan -- Periodic solutions to $O(2)$-symmetric variational problems: $O(2) \times S^1$- equivariant gradient degree approach; J. F. Bonnans and N. P. Osmolovskii -- Quadratic growth conditions in optimal control problems; J. M. Borwein and S. Sciffer -- An explicit non-expansive function whose subdifferential is the entire dual ball; G. Buttazzo and G. Carlier -- Optimal spatial pricing strategies with transportation costs; R. A. C. Ferreira and D. F. M. Torres -- Isoperimetric problems of the calculus of variations on time scales; M. Foss and N. Randriampiry -- Some two-dimensional $\mathcal A$-quasiaffine functions; F. Giannessi, A. Moldovan, and L. Pellegrini -- Metric regular maps and regularity for constrained extremum problems; V. Y. Glizer -- Linear-quadratic optimal control problem for singularly perturbed systems with small delays; T. Maruyama -- Existence of periodic solutions for Kaldorian business fluctuations; D. Mozyrska and E. Paw'uszewicz -- Delta and nabla monomials and generalized polynomial series on time scales; D. Pallaschke and R. Urba'ski -- Morse indexes for piecewise linear functions; J.-P. Penot -- Error bounds, calmness and their applications in nonsmooth analysis; F. Rampazzo -- Commutativity of control vector fields and ""inf-commutativity""; A. J. Zaslavski -- Stability of exact penalty for classes of constrained minimization problems in finite-dimensional spaces. (CONM/514)

International Conference On Differential Equations Berlin Germany 1 7 August 1999

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Author : Bernold Fiedler
language : en
Publisher: World Scientific
Release Date : 2000

International Conference On Differential Equations Berlin Germany 1 7 August 1999 written by Bernold Fiedler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Differential equations categories.

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences

Continuation And Bifurcations Numerical Techniques And Applications

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Author : Dirk Roose
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Continuation And Bifurcations Numerical Techniques And Applications written by Dirk Roose and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989